Testing Compliance with Occupational Exposure Limits for Airborne

Testing Compliance with
Occupational Exposure Limits
for Airborne Substances
British Occupational Hygiene Society
Pride Park Derby
DE24 8LZ, UK
www.bohs.org
Nederlandse Vereniging voor
Arbeidshygiëne
Postbus 1762,
5602 BT Eindhoven
The Netherlands
www.arbeidshygiene.nl/
Originally published September 2011
This edition December 2011
See p51 for amendment history
2
Testing Compliance with Occupational Exposure Limits
for Airborne Substances
Contents
Preface: What is this document for?
Introduction:
MOST IMPORTANT - READ THIS FIRST
SUMMARY
Chapter 1.
Conducting a survey for exposure evaluation
1.1 The initial evaluation of the workplace
1.2 Measurement methods
Chapter 2.
The problem of variability
2.1 Variability of exposure
2.2 Some evaluation software
2.3 How many measurements?
2.4 The problems of between-worker and within-worker variability
2.5 The problem of compliance
2.6 The approach of this guidance
Chapter 3.
Recommended method of measuring compliance
3.1 Principles
3.2 Selection of similarly exposed groups (SEGs)
3.3 Screening test
3.4 Group compliance test
3.5 Analysis of variance (ANOVA)
3.6 Individual compliance test
3.7 Treatment of values <LoQ
3.8 Reassessment
3.9 Use of the results
Chapter 4.
Shortcuts and their limitations.
4.1 Shortcut 1: Taking a few samples from the most exposed worker and using
evaluation software
4.2 Shortcut 2: Taking a few samples and seeing if they are <OEL/3
4.3 Shortcut 3: AIHA and Bayes
Appendix 1.
Calculations for the group and individual compliance tests
Amendment history
3
4
Preface: What is this document for?
When repeat measurements are made of exposures to airborne substances in the workplace, it
often happens that most results are within a fairly narrow range, but a few results scatter on the
high side, sometime four or five times the median or even higher, for no clear reason. This is not
due to a failure of control, but happens because there is a statistical chance that the many factors
which determine exposure sometimes combine in a way which produces an outlying result. It is a
problem partly because occupational exposure limits (OELs) are defined as sharp cut-offs, values
which must not be exceeded, taking no account of occasional outliers. (Section 2.5 discusses how
regulations define “compliance”.) So the law theoretically expects exposure to be controlled below a
fixed threshold, when in reality even well-controlled exposure cannot be made to behave like this –
outliers inevitably occur. In practice, properly trained enforcers usually take into account accepted
good practice and look beyond the simple numbers to the reality of control.
There are also other complications in estimating exposure in relation to OELs. Various attempts
have been made to provide guidance in this difficult problem, such as the pioneering NIOSH
document Leidel et al (1977), BOHS Technical Guide 11 (BOHS, 1993), and the European Standard
EN689 (CEN, 1995). Each of these has fairly soon become out of date because of advances in
understanding of how exposure behaves, and improved strategies for dealing with this.
This document aims to give guidance to occupational hygienists and others on measurement
strategies for determining compliance with occupational exposure limits. It does not give general
guidance on conducting a survey of exposure in the workplace - Chapter 1 refers to documents that
do that. It aims to be a guide to good practice on measuring compliance with an OEL in the light of
present knowledge, taking into account the variability of the exposures of individuals and groups. It
is assumed that you will not use this document unless you have already surveyed the workplace and
decided that you should to do a proper test of whether any exposures exceed the OEL.
The layout of the guidance is as follows. Chapter 1 briefly indicates where to find information on
conducting a survey of exposure in the workplace. The rest of the document is about what to do if
as a result of the survey you decide that exposure may exceed an OEL. Chapter 2 outlines the
problem of exposure variation and how it relates to legal definitions of exposure limits, and Chapter
3 and Appendix 1 describe a recommended assessment and data treatment method. Chapter 4
outlines simpler evaluation methods and their strengths and shortcomings. It comes out clearly in
Chapter 3 that getting reliable answer on compliance with an exposure limit requires more
measurement than many hygienists are used to. The most important part of the guidance is
therefore the Introduction, which aims to put compliance testing in its proper place in achieving
good control of risk, which is the hygienist’s proper job and the aim of good legislation.
This guidance has been produced by a working group of the British and Dutch occupational hygiene
societies (BOHS and NVvA). The two societies make this publicly available in the belief that this
represents good professional practice. However, the societies accept no liability for any
consequences of its use. The user is responsible for ensuring that risk from airborne substances is
controlled as the law requires.
5
In the public consultation on a draft, many other people made major and valuable comments which
led to this revised version, and the working group thanks them. Also, particularly important
contributions came from Andrew Garrod (formerly of the British Health and Safety Executive),
Jérôme Lavoué (of the University of Montreal), Huib Arts, and Margreet Sturm
From past experience, this document is likely to require fairly frequent revision to cope with
improved understanding of the statistics of workplace exposure and the best strategy for
measurement. We hope however that it will be useful contribution at the moment and a good basis
for future development.
For BOHS:
Trevor Ogden (co-chair)
Adrian Hirst
John Ingle
Andrew Kennedy
Martie van Tongeren
For NVvA:
Hans Kromhout (co-chair)
Kees Hommes
Joost van Rooij
Theo Scheffers
Erik Tielemans
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Introduction
Most important – read this first
This guidance is about measuring compliance with exposure limits for airborne substances, but it is
ESSENTIAL that this is only considered in a wider context of assessing and controlling risk. In the
European Union, the law requires this – the Chemical Agents Directive (EU, 1998) and the
Carcinogens Directive (EU, 2004) both require effective control as well as compliance with limits –
and national regulations in the member states implement these requirements.
If you are a hygienist, remember that proving that an exposure limit is probably complied with is
likely to be expensive and time-consuming, There is no point in doing it unless the occupational
hygiene methods of control are also applied – the law requires this as well as compliance with the
exposure limit, and applying this guidance without also applying good control practice may be
wasted time and effort.
If you are an employer or someone concerned about a workplace, have the principles of good
practice been applied? For example, here are some of the principles taken from guidance on the
British Control of Substances Hazardous to Health Regulations (HSE, 2005).






Design and operate processes and activities to minimise emission, release and spread of
substances hazardous to health.
Take into account all relevant routes of exposure – inhalation, skin absorption and ingestion
– when developing control measures.
Choose the most effective and reliable control options which minimise the escape and
spread of substances hazardous to health.
Check and review regularly all elements of control measures for their continuing
effectiveness.
Inform and train all employees on the hazards and risks from the substances they work with,
and use of control measures.
Ensure that the control measures for substances do not introduce some other sort of risk.
Applying these principles properly is often a skilled business. National occupational hygiene
associations will usually advise on where to find competent help. For a list of associations, see the
International Occupational Hygiene Association website http://www.ioha.net/ . In Britain the British
Occupational Hygiene Society maintains a list of consultancies with qualified and experienced
occupational hygienists who can advise on this, at http://www.bohs.org/OHServices-directory/, and
in the Netherlands contact NVvA at [email protected]. Using a consultant may be much
cheaper and more successful than installing expensive and possibly ineffective control equipment.
An enforcement agency will usually look at the whole of the control procedures together. Applying
this guidance will enable the employer or hygienist to demonstrate that exposure limits are
7
probably complied with, but, as well as looking at the numbers, an enforcer is likely to ask: (1) are
engineering methods working?; (2) are engineering controls and other procedures maintained?; (3)
are there weaknesses in the way good practice is complied with? As explained in this guidance,
statistical fluctuations may lead to occasional measurements above the exposure limits even under
good overall control, but an enforcer will generally pay more attention to the answers to these
questions about good control than to statistical outliers.
This guidance is about finding out whether exposures comply with exposure limits. The guidance
shows that doing this thoroughly enough to be fairly certain of the answer requires much more
measurement than is usually done in a quick hygiene survey. There is no point in doing this unless
proper attention is also paid to good control practice.
8
Summary
The aim is to provide hygienists and employers with guidance on testing compliance with 8-hr
occupational exposure limits (OELs) for airborne substances. It is assumed that a general workplace
survey has been done, resulting in a need to test exposure against an OEL..
The problem is that OELs are usually defined as sharp boundaries that must not be exceeded, but
the variability of exposure means that occasional high results occur even where the exposure is
generally well controlled. The guidance assumes that an OEL may be regarded as complied with if
the probability of exposure exceeding the OEL is <5%, always remembering that EU law requires
that effective control measures are applied whether or not the OEL is complied with.
The method has five steps.
(1) Divide the workforce into
similarly exposed groups (SEGs).
(2) Take 3 representative personal
exposure measurements from
random workers in the SEG. If all
three exposures are <0.1xOEL, it can
be assumed that the OEL is complied
with. If at this stage or any later one
any result is >OEL, the OEL is not
complied with.
(3) Do a group compliance test. Take
at least 6 more samples from the
SEG, at least 2 per worker from
workers picked at random. Use all 9
(or more) samples to apply a test
which establishes, with 70%
confidence, that there is <5%
probability of any random exposure
in the SEG being >OEL.
(4) Do an analysis of variance on the
9 (or more) results to establish
whether the between-worker variance is >0.2 x total variance. If it is, then step 5 must be added.
(5) Analyse the 9 (or more) results to do an individual compliance test. There should be <20%
probability that any individual in the SEG has >5% of exposures > OEL.
If the OEL is not complied with, further control measures should be applied. If the OEL is complied
with, a periodic monitoring programme should be started, with frequency depending on the test
results.
An appendix gives examples of the necessary calculations in Microsoft Excel.
Three shortcut methods and their limitations are discussed.
9
Chapter 1.
Preliminary considerations
1.1 The initial evaluation of the workplace
This guidance starts from the assumption that a general evaluation of exposure has been done and
measurements are now required to determine whether exposure exceeds the OEL. The methods
presented in this document therefore come at the end of a substantial process, which is likely to
include:
 obtaining a general overview of the workplace and its layout, the tasks carried out and the
control measures in place (and whether more control is reasonably practicable);
 considering how these processes vary, perhaps from shift to shift and operator to operator,
and how this might affect exposures;
 consideration of what health and safety precautions are involved in carrying out the
evaluation;
 walk-through surveys with direct-reading instruments;
 refinement of estimated exposures using models such as Stoffenmanager
https://www.stoffenmanager.nl/default.aspx ;
 consideration of what occupational exposure limits (OELs) apply and whether they may be
exceeded (in which case this guidance can be applied);
 consideration of what periodic monitoring might be required;
 communication to management and workforce.
This guidance does not deal with these issues. Most are explained fully in guidance on assessing and
managing exposure published by the American Industrial Hygiene Association (AIHA, 2006). A
modern text on occupational hygiene should also be consulted, such as Cherrie et al (2010), which
gives wide-ranging guidance on assessment and control, including detailed checklists on carrying out
a workplace survey. Since the AIHA guidance was published, Hewett et al (2006) and Ramachandran
(2008) have described a way of using a few measurements to improve exposure management. This
is summarised in section 4.3 below.
It is important that people carrying out the assessment are professionally competent to do so – the
organisations referred to in the Introduction may be consulted for advice on this.
If as a result of this general evaluation of workplace exposure it is considered that OELs may be
exceeded, the guidance in the rest of this document may be used to determine if this is likely to be
true, but this guidance assumes that the above initial evaluation has been done.
What OELs apply will depend on the country where exposure occurs. The larger countries in the
European Union (EU) will all have their own lists, which will incorporate EU limits. GESTIS
http://www.dguv.de/ifa/en/gestis/limit_values/index.jsp gives a consolidated list of OELs from
various major jurisdictions.
10
As explained in Section 3.2, the information gained in the survey should be useful in forming
similarly exposed groups (SEGs) at the stage of determining compliance with the OELs.
1.2 Measurement methods
An important preliminary step in measurement is selection of the sampling and analytical method.
GESTIS http://www.dguv.de/ifa/en/gestis/analytical_methods/index.jsp lists validated sampling and
analytical methods from EU countries for 123 substances. Another important source is the US
National Institute for Occupational Safety and Health (NIOSH) Manual of Analytical Methods
http://www.cdc.gov/niosh/nmam/ . These sources outline validated regimes of sampling and
laboratory analysis for quantifying exposure concentrations of the hazardous substance through
inhalation. However, where no methods exist e.g. in the case of a new or novel substance, it might
be necessary to develop and validate an in-house method.
AIHA (2006) and Cherrie et al. (2010) give advice on how to take samples, and some of the analytical
methods just mentioned give advice on sampling. More technical details on assessment of airborne
contaminants are given by Ramachandran (2005). National OEL lists should define the period to
which the OELs apply, and should give instructions on how the exposure should be calculated for
comparison with the OEL. Further details are given in Chapter 3.
Usually samples will need to be sent to a laboratory for analysis. In all cases there will be a lower
limit to the amount of the substance that the analytical technique can detect and what can be
quantified, and a competent laboratory must be able to tell you what this is. When divided by the
volume of air from which the substance was collected, the analytical quantification limit gives a limit
of quantification (LoQ) of concentration of the substance in the air. Wherever possible, the
analytical method and the volume sampled should be chosen to ensure that the LoQ is less than
one-tenth the OEL (LoQ < 0.1 OEL). The treatment of measurements below the LoQ is discussed in
section 3.7.
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Chapter 2
The problem of variability, and the place of this guidance
2.1 Variability of exposure
Anyone who has measured exposures in a workplace will be aware that the exposure varies,
whatever measurement period is chosen and whatever is done to keep conditions constant. The
variation is usually much greater than can be accounted for by analytical error. Fig 1 shows a typical
case, based on measurements made in the weaving sheds of a cotton mill (Ogden et al, 1993). The
results peak at relatively low exposures, with one or two results at several times the most frequent
exposure.
This kind of distribution can usually be fitted well by a log-normal curve.1 Fig 2 shows such a curve
fitted to the data in Fig 1. Because there is a limited number of exposure measurements in Fig 1 (26
altogether) the fit is rough, but if we were to make more and more measurements in this
environment under the same conditions, Fig 1 would become a smoother curve and would probably
look more and more like Fig 2 as the number of measurements increased. The usefulness of fitting
the curve is that it enables us to estimate various parameters of this environment (and their likely
errors) that we could only get exactly by taking a very large number of measurements. The curve
shown in Fig 2 was fitted to the Fig 1 data using a spreadsheet IHSTAT™which is made available by
the American Industrial Hygiene Association (AIHA). More details of this and other software are
given in Section 2.2 below.
Fig 2 shows several interesting features. The mean exposure estimated from the curve is marked as
“est AM” and in this case is 0.62 mg/m3 . (IHSTAT calculates values to three decimal places, but we
round this to two in this chapter, although even this precision will often be unjustified.) Because of
the variability of the results and the limited number of measurements, there is some uncertainty on
this, and the confidence limits on the mean are shown (LCL and UCL). IHSTAT estimates that we can
be 95% certain that if we took a very large number of measurements in this environment, the mean
would be between 0.52 and 0.79 mg/m3. The curve further predicts that 95% of measurements
would be less than 1.38 mg/m3. However, this 95th percentile is not known very precisely unless
there is a very large number of measurements, and all we can say from these 26 is that we can be
95% certain that the true value of the 95th percentile is less than 1.98 mg/m3. These values and
others are all tabulated on IHSTAT when we input these data. All of this assumes that the measured
exposures are log-normally distributed, but this is usually found to be the case.
IHSTAT enables us to input an occupational exposure limit for comparison with the data, and for
illustration purposes we have supposed that the OEL is 1.7 mg/m3. The programme estimates that
2.2% of the fitted log-normal curve lies above this value. From Fig 1 it can be seen that one of our 26
results (3.8%) was above this value, but clearly it could by chance easily have been 0 or 2 results, and
1
This is related to the familar bell-shaped normal curve – if the horizontal axes in Figs 1 and 2 were plotted as
the logarithms of the concentration, the distribution would look like a normal curve .
12
if the distribution is really lognormal then the fitted curve gives a better estimate of what is likely to
happen at the 95th percentile than our unprocessed measurements.
Fig 1. Personal exposure measurements in weaving at a
cotton mill.
10
9
Number of samples
8
7
6
5
4
3
2
1
0
Exposure mg/m3
Exposure mg/m3
Fig 2. Log-normal curve fitted to the data13in Fig 1 using the AIHA
tool IHSTAT™
2.2 Some evaluation software
IHSTAT™, the software used in Section 2.1, is made available by AIHA at
http://www.aiha.org/insideaiha/volunteergroups/EASC/Pages/EASCTopics.aspx . This is also
illustrated in section 2.3, and we acknowledge AIHA’s kind permission to use this copyright material.
IHSTAT is a trade mark of AIHA. However, there are several other pieces of software available,which
may have useful advantages, and if you analyse data of this type we encourage you to also look at
these. A long-established example which has recently been updated is HYGINIST, downloadable
from http://www.tsac.nl/downen.html . An example produced by Paul Hewett in the US is
IHDataAnalyst, with a more limited free version IHDataAnalyst-LiteEdition, both downloadable from
http://www.oesh.com/software.php . Perhaps the most comprehensive is AltrexChimie, produced
in France by the Institut National de Recherche et de Sécurité, downloadable free from
http://www.inrs.fr/inrs-pub/inrs01.nsf/IntranetObjectaccesParReference/Dossier%20Altrex/$File/print.html . In Altrex Chimie it is permissible to enter
the data in any order with, for example, who was sampled and on what day. It handles values
below the Limit of Quantification (LoQ), and it produces graphs that can be pasted into a report, and
has other useful features. It is in French of course, but the tutorial in the Help folder is fairly easy to
follow for users with a basic knowledge of the language.
2.3 How many measurements?
Although we have seen that 26 measurements are too few to characterize exposure exactly, it is
often thought to be impracticable to take anything like this number. What would happen if we only
took say a quarter of this number?
Fig 3 shows the curve fitted by IHSTAT to 7 results taken at random from the set of 26 used in Figs 1
and 2. The arithmetic mean estimated from the curve is now 0.63 mg/m3, which is very close to the
earlier value of 0.62. The confidence limits on this mean are however much wider than before –
0.40 to 1.77 mg/m3 – compared to 0.52 and 0.79 mg/m3. In fact the main effect of using a small
number of measurements is that the estimates of parameters are much less certain. The best
estimate of the 95th percentile is 1.77 mg/m3, compared with 1.38 before, but the uncertainly of this
number is hopeless – all that we can say is that we are 95% certain that the 95th percentile lies below
6.9 mg/m3. We think that the 95th percentile is just above the exposure limit of 1.7 mg/m3, but it
may be four times that. (IHSTAT drew the curve large enough to include 6.9 mg/m3 on the horizontal
axis. To make Fig 3 comparable with Fig 2, we just took the bottom section of the curve, and
stretched; this is why the lettering appears distorted.) This illustrates that measuring compliance
with an OEL requires a lot more measurement than generally assumed. We will discuss how
compliance is defined in section 2.5, but first we must mention the importance of individual
variation.
14
Exposure mg/m3
Fig 3. The lognormal distribution fitted by IHSTAT to seven
measurements taken at random from the 26 used to produce Fig 2.
2.4 The problems of between-worker and within-worker variability
An important complication is that two workers doing the same job will not have the same exposure,
because of minor differences in work pattern or equipment. This phenomenon, known as betweenworker variability, means that measurements of one worker’s exposure cannot simply be assumed
to apply to others doing nominally the same job. Of course, the hygienist will wish to correct any
evident faults which increase exposure, but experience shows that even after this is done betweenworker variability is sometimes not eliminated. Fig 4 illustrates the sort of difference that may
occur. Rather more obviously, exposure varies from shift to shift, giving rise to within-worker
variability. When they can be separated, both types of variation tend to follow lognormal patterns,
and together they will give overall variation like that illustrated in Fig 1.
The usual procedure in assessing exposure where more than one worker is involved is to divide the
workforce into similarly exposed groups (SEGs) (see section 3.2), and in some way or other to try to
take samples which are representative of the group and representative of the work done. But
because of between-worker variability, care must be used in applying a tool like IHSTAT to the whole
group. The 95th percentile of the whole group may underestimate or overestimate the percentile for
individual workers. These problems have been extensively investigated, especially in the past 20
years, and details are given in standard texts (e.g., Kromhout et al 2005; Ramachandran, 2005;
Rappaport and Kupper, 2008). They must be taken into account in any compliance-testing
procedure.
15
Number of samples
10
Worker 1.
Mean 0.62 mg/m3 95th centile 1.38
mg/m3
8
6
4
2
0
Exposure mg/m3
Number of samples
Worker 2.
8
6
Mean 0.78 mg/m3; 95th centile 1.88
mg/m3
4
2
0
Exposure mg/m3
Number of samples
12
10
Worker 3.
Mean 0.54 mg/m3; 95th centile 1.28
mg/m3
8
6
4
2
0
Exposure mg/m3
Fig 4. Simulated exposures of three workers in the same occupational group
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2.5 The problem of compliance
The central problem of compliance testing is illustrated by Figs 1, 2, and 4. A few measurements will
determine the usual exposure, but some results occur which are three or more times the usual
value, sometimes for no obvious reason, and in theory the upper limit to the distribution can be very
high. Workplace regulations usually apply OELs as absolute limits, with no excursions allowed:
examples are the Chemical Agents Directive (EU, 1998), the Carcinogens Directive (EU, 2004), and, in
Britain, the COSHH Regulations (HSE, 2005). So if several measurements are below the exposure
limit, how can an employer be sure that the next one will not be above it and show non-compliance?
Defining OELs as sharp cut-offs has two bad consequences. First, it makes it impossible in principle
for an employer to establish a monitoring programme which will prove that the exposure limit will
always be complied with, however often it has happened in the past. Second, it is a disincentive to
monitoring exposure. If a couple of measurements show compliance, then it seems better to stop
at that point and not risk a higher result next time. When OELs were first defined they were not
applied in this way, but current EU regulations treat them as sharp cut-offs, and we must cope with
this.
OELs apply to all workers, not just to a group, so any monitoring programme must take into account
between-worker variability. It is not permissible to offset low exposure of one worker against high
exposure of another: all must comply.
2.6 The approach in this guidance
Faced with the variability problem outlined above, professionals have often regarded it as
satisfactory to show that the 95th percentile of the exposure distribution is probably below the OEL.
This sometimes gets regulatory backing. For example, although the Permissible Exposure Limit (PEL)
for formaldehyde in the United States is an absolute limit, the US Occupational Safety and Health
Administration says that “a properly designed sampling strategy showing that all employees are
exposed below the PELs, at least with a 95 percent certainty, is compelling evidence that the
exposure limits are being achieved provided that measurements are conducted using valid sampling
strategy and approved analytical methods” (OSHA, 2011). We are unaware of any such statement in
Europe, but, as explained in the Introduction, enforcement authorities will usually look at exposure
limits in the context of control practice, looking at a monitoring record alongside the questions: (1)
are engineering methods working?; (2) are engineering controls and other procedures maintained?;
(3) are there weaknesses in the way good practice is complied with?
This guidance therefore generally tests the 95th percentile. It does not take away the legal obligation
that an OEL must not be exceeded. However, it aims to give hygienists and employers a way of
demonstrating that there is a low probability of non-compliance, without requiring disproportionate
resources. The records of a programme like this can be put alongside answers to the three
questions above as evidence of compliance with good practice.
17
Chapter 3.
Recommended method of measuring compliance
3.1 Principles
The method in this chapter should only be applied and considered along with good control practice,
as outlined in the Introduction to this guidance.
Almost all workplace occupational exposure limits (OELs) are defined as either 8-hr mean levels or
short-term (usually 15 minutes) levels, and apply to personal exposure, ie exposure measured with
equipment carried by the worker which samples contaminants from air near the nose and mouth.
The procedures in this chapter describe how to compare measurements with 8-hr (shift) OELs.
Sources such as Cherrie et al. (2010) and AIHA (2006) describe how to take valid samples. For
comparison with the OEL, all significant exposure periods during the shift should be included in the
sample. For comparison with the OEL, the amount of the material collected should be divided by the
volume of air that would have been collected if the sampling had continued for 8 hr. More details
and examples of this sort of calculation are given in Annex B of EN 689 (CEN, 1995). References to
exposure measurements in this chapter mean shift-length average exposures calculated in this way.
As explained in chapter 2, compliance tests are often applied to similarly exposed groups (SEGs), but
workers who are doing the same job are often unexpectedly found to have different exposure
patterns. In this guidance we therefore test the SEG for compliance with the OEL, and, if there is
evidence that different SEG members have different exposures, we test individual compliance. The
two measures used are as follows.
Group compliance. The group complies if, with 70% confidence, <5% of the exposures in the SEG
exceed the OEL.
Individual compliance. The SEG complies in terms of individual exposure if there is <20% probability
that any individual has >5% of his or her exposures exceeding the OEL.
The method has five stages: selection of similarly exposed groups (section 3.2), a screening test (3.3),
a group compliance test (3.4), and an individual compliance test (3.6) if an analysis of variance (3.5)
shows that differences between individual exposure patterns makes this desirable. Fig 5 is a
flowchart illustrating the process. Calculation methods are illustrated in Appendix 1.
18
Form SEG
(Section 3.2)
Take 3 samples
(Section 3.3)
Screening test
Improve
controls
Yes
No
Are any of
the three > OEL?
(Section 3.3)
No
Are all three samples
<0.1 OEL? (Section 3.3)
Yes
No
Take 6 more samples
(Section 3.4)
Is the group
compliance test passed?
(Section 3.4)
Group compliance test
Yes
Apply ANOVA
(Section 3.5)
No
Individual
compliance
Is the
test
individual compliance
test passed?
(Section 3.6)
Are between-worker
differences important?
(Section 3.5)
Yes
Test individual compliance
(Section 3.6)
Yes
Routine monitoring
(reassessment)
(Section 3.8)
Fig.5. Flowchart of the process
19
No
3.2 Selection of similarly exposed groups (SEGs)
OELs apply to every worker, but where different workers are carrying out the same task in the same
way, it is usual to limit the number of samples to be taken by dividing the workforce into similarly
exposed groups (SEGs), and to make measurements on only some of the members of each group.
Mulhausen and Damiano (2006) define a SEG as “A group of workers having the same general
exposure profile for an agent because of the similarity of the materials and processes with which
they work, and the similarity of the way they perform the task(s).” Clearly, allocating workers to a
SEG will require careful examination of these three factors – the materials, the processes, and the
ways of working. Using job titles to allocate workers to a SEG will almost certainly be insufficient.
As explained in Chapter 1 above, a decision to test compliance with OELs using this guidance should
involve a detailed initial survey, and the information gained in the survey will be useful in forming
SEGs. If a person performs different tasks in different shifts, they he or she should be allocated to
more than one SEG. Mulhausen and Damiano discuss SEG construction in detail, including difficult
cases such as non-routine and non-repetitive tasks, and we recommend that their account is
consulted in case of doubt.
If it is clear that if one or more people who are doing a task are known to be doing it in a different
way from others, then by definition they should not be included in the same SEG as the others. It
may be appropriate to put someone in a one-person SEG and proceed to compliance testing, or to
conduct a preliminary examination to see which method of work produces least exposure and then
to consider appropriate staff training.
When exposure measurements within a SEG are available, perhaps after the compliance testing
process, it is possible to test whether the allocation of workers to a SEG was successful, using
analysis of variance techniques. A feature of the AltrexChimie software, mentioned in Section 2.2, is
that it will do this and report whether inter-worker differences are significant (Section 2.4). It also
permits the user to test whether members of a SEG are really “similarly exposed” by permitting the
user to set a geometric standard deviation judged to be acceptable for a SEG and to test if the group
meets it.
3.3 Screening test
If LoQ > 0.1 x OEL (see section 1.2) it will not be possible to apply the screening test – the evaluation
should go straight to the group compliance test (Section 3.4).
For the screening test, take three shift-length exposure measurements on workers selected at
random from the SEG. If there are fewer than three workers in the SEG, the measurements will have
to be spread over more than one shift, and one or more workers measured twice.
If all three results are <0.1 x OEL, then compliance with the OEL can be assumed to be satisfactory,
and no further measurements are required immediately. However, routine repeat surveys should
be planned (called reassessment by AIHA (2006) and periodic measurements by EN 689 (CEN, 1995))
- see section 3.8 for further details of this.
If any of the three measurements exceeds the OEL, and there is no clear reason why the
measurement is invalid, then clearly there is non-compliance and the programme may be
20
terminated. However, if there are reasons to believe that the result is invalid for some reasons, it
should be discarded and the group compliance test should be done.
This screening test is taken with slight modification from Annex 1 of the French regulatory scheme
(France, 2009), which has been validated by the Institut National de Recherce et de Sécurité (see
INRS, 2008).
3.4 Group compliance test
The group compliance and individual compliance tests require the following exposure
measurements from each SEG tested:
a minimum of 9 (or more if convenient) measurements;
at least 2 samples and if possible at least 3 shift measurements from each worker selected;
if there are > 2 workers in the SEG, measure exposure of at least 3 workers;
if not all workers are to be measured, select those measured at random.
If the 3 screening test measurements are still valid, they may be used again in the group and
individual tests, with more measurements to make up the minimum of 9. Similarly, if other valid
samples are available, for example as part of a long-term monitoring programme, they may be used.
Compliance has often been estimated by comparing the 95th percentile of the exposure distribution
with the OEL (section 2.6). To be certain that this is true would require a very large number of
samples to be taken. Work by the Institut National de Recherche et de Sécurité in France (INRS,
2008), and by Jérôme Lavoué of the University of Montreal (Lavoué, to be published), has shown
that the test can be applied with a modest number of samples if we require 70% confidence that less
than 5% of the exposures are above the OEL. This gives a balance between probability of declaring
non-compliant a distribution which would prove compliant if a large number of samples were taken,
and declaring compliant a distribution which would prove non-compliant if there were a large
number of samples.
The test is applied as follows
Calculate the geometric mean MG and the geometric standard deviation sG of all of the exposure
measurements in the SEG. If the n individual shift exposure levels are a1, a2, a3,...an, these are
log MG = (log a1 + log a2 + log a3 ... + log an)/n
(equation 1)
log sG = √ { * (log a1 – log MG)2 + (log a2 – log MG)2 + (log a3 – log MG)2 ... + (log an – Log MG)2] / (n-1) }
(2)
These can be worked out using a scientific calculator; or the method in Appendix 1 can be applied.
We then calculate the parameter U (also shown in Appendix 1)
U = [ log (OEL) – log MG ] / log sG
(3)
U is then compared with the limiting values given in Table 1. If U is less than the limiting value for
the number of exposures given, the OEL is not complied with.
21
Table 1. Limiting values of U. The OEL is not complied with if U calculated from equation (3) is less
than the limiting value given here. Limiting values of U for other sample numbers are given in
Annex 2 of France (2009).
Number of exposure measurements
Limiting value of U
9
2.035
10
2.005
11
1.981
12
1.961
13
1.944
14
1.929
15
1.917
If the OEL is complied with by the group compliance test, it is necessary to perform an analysis of
variance (section 3.5) to decide whether individual compliance should be tested.
(The group compliance test is taken from France (2009). It assumes that the exposures are lognormally distributed, and uses the estimates of the geometric mean and the geometric standard
deviation to test whether we can be sure, with 70% confidence, that less than 5% of the exposures
are above the OEL.)
3.5 Analysis of variance (ANOVA)
The total variation of exposure in the SEG is composed of temporal variation of each individual
worker’s exposure about that individual’s mean and the variation in mean exposure between
workers. If the between-worker variation makes an important contribution to the total variation it is
necessary to test individual compliance (as defined in section 3.1).
We compare the between-worker variance with the total variance using a standard analysis of
variance ANOVA procedure. This is explained in any statistics textbook, such as Wonnacott and
Wonnacott (1990). Appendix 1 illustrates calculation using Microsoft Excel. If the between-worker
variance is equal to or more than 20% of the total variance, then the individual compliance test in
section 3.6 should be applied.
(Computer simulations by Jérôme Lavoué of the University of Montreal, made available to the
working group, have found that if the SEG passes the group compliance test in section 3.4, and the
between-worker variance is less than 20% of the total variance, then the individual compliance test
will also be passed, so there will be no need to perform that test (Lavoué, to be published). ANOVA
22
can be used to test whether the between-worker contribution to variance is significant at the 5%
level, but Lavoué’s simulations have found that this does not add anything to the 20% test.)
3.6 Individual compliance test
If it were possible to construct SEGs perfectly, there would of course be no difference between
exposure patterns of the members of the SEG, and the group compliance test would effectively test
the exposure patterns of individual members of the SEG. However, differences can be subtle and
only emerge in a sampling programme, so the results must be examined to see if differences have
emerged, by testing individual compliance.
The individual compliance test may be omitted if the results of the analysis of variance in section 3.5
show that the between-worker variance is <20% of the total variance. If this condition is met then it
can be assumed that the exposure patterns of the members of the SEG are sufficiently similar for the
results of the group compliance test to be enough to characterize exposure. Otherwise, individual
compliance should be calculated.
As defined in section 3.1, individual compliance requires <20% probability that any individual has
>5% of his or her exposures exceeding the OEL. We estimate this by calculating the parameter
H = [ log (OEL) – ( log MG + 1.645 sw ) ] / sb
(4)
from Hewett (2005), Appendix A, and then calculating the fraction of the distribution which lies
above this value. By our definition (section 3.1) our individual compliance criterion is met if this
fraction is <0.2.
This procedure assumes that the logarithms of the exposures of each worker are normally
distributed (ie that their exposures are log-normally distributed) and that the geometric means of
the exposures of the individual workers are also log-normally distributed. sw2 and sb2 are
respectively the within-and between-worker variances of the distributions of logged values. The
calculation of this is illustrated in Appendix 1 to this guidance, using Microsoft Excel.
It might be thought that we need to be sure that no workers are in this position, not just <20%, but
because the test is actually applied to log-normal distributions fitted to the exposure measurements,
the result of this calculation is never zero. Another way of expressing our individual compliance
criterion is that >80% of the SEG members have at least 95% of their exposures < OEL.
It should be noted that in sections 3.5 and 3.6 we have applied two completely different tests
involving 20% thresholds, which should not be confused. In section 3.5 we said that individual
compliance should be tested if between-worker variance > 20%, and in this section we have said that
<20% of individuals should have >5% of exposures >OEL.
Other measures have been used as measures of compliance, for example the probability of
overexposure (Kromhout et al., 2005), defined as the chance that a random worker’s long-term
mean exceeds the OEL. This has a logic in health terms for substances whose effect is due to longterm cumulative exposure, but because almost all workplace OELs are defined in terms of 8-hr or
15-min exposure, we have not used overexposure here.
23
3.7 Treatment of values < LoQ
Every attempt should be made to use analytical methods and sample volumes that keep the LoQ <
0.1 x OEL. If this is done, the tests in sections 3.3 to 3.6 can be applied without adjustment.
However, with some substances it may prove impossible to keep the LoQ this low.
The treatment of values < LoQ in statistical analysis of sampling results is controversial, and is still an
active field of research (Helsel, 2005 and 2010), so it is not possible to firmly recommend one
method. A simple method is given below. But in general, if any way of treating values <LoQ
discussed by Helsel or another reputable source gives a non-compliance decision, non-compliance is
the decision.
Regression methods are available which use the distribution of results >LoQ to estimate the
distribution <LoQ, for example applied by HYGINIST and AltrexChimie (see section 2.2). Methods for
censored samples from lognormal populations combined with goodness-of-fit tests (eg Schneider,
1986) can be used for the group compliance test (section 3.4). The unbiased censored approach is
included in e.g. HYGINIST. For the individual compliance test (section 3.6) a sound treatment of
values < LoQ does not exists at the moment.
If no better test is available, the following is suggested, but it has not been fully validated. If more
than 10% of the exposure values are < LoQ, the calculations in sections 3.4 and 3.6 should be carried
out three times, with < LoQ values treated this way:
(1) substitute all <LoQ values by 0.25xLoQ;
(2) substitute them all by the LoQ;
(3) substitute half of them by 0.25xLoQ and half by LoQ.
If all three approaches lead to a compliance decision, this can be accepted, but if any give noncompliance, non-compliance is the decision.
It is not recommended simply to substitute LoQ/2 or LoQ/√2 for each value below the LoQ (Helsel
2010).
3.8 Reassessment
A survey which establishes that the OELs are complied with should be followed by occasional
reassessment, and if possible a programme for this should be planned and agreed with management
or the responsible authority at the end of the initial survey. Such a programme is called “periodic
measurements” by EN689 (CEN, 1995) and “reassessment” by AIHA (2006).
A reassessment programme should have the general aim of ensuring that control remains
satisfactory, and checking compliance with the OEL will be part of this. The programme should
therefore take into account changes in the factors affecting exposure, including changes in process,
substances, ways of organising work such as shift patterns, and substantial changes in personnel.
However, those involved may be unaware of changes affecting exposure, such as gradual
deterioration in ventilation equipment, or subtle changes in ways of working, so there should be an
agreed programme to reassess compliance with the OEL even in the absence of obvious change.
24
The interval for reassessment depends mainly on professional judgement if there are no obvious
signs of change, and will depend upon the industry and the processes involved. AIHA (2006), CEN
(1995), and France (2009) all make somewhat different recommendations, and from these the
following intervals for reassessing compliance with OELs should be considered. The geometric mean
(GM) is calculated for the results obtained in sections 3.3 and 3.4, plus any later relevant results.
GM <0.1 OEL
0.1 OEL < GM < 0.25 x OEL
0.25 OEL <GM< 0.5 OEL
0.5 OEL <GM
2 yr
1 yr
6 months
3 months
However, these intervals should be interpreted taking into account the following.



Effective control measures should be applied by those responsible for the workplace at all
times, bearing in mind that in the European Union and many other jurisdictions the law
requires effective control as well as compliance with OELs. Those responsible for the
workplace must therefore be aware of the relevant important measures.
The intervals will depend on the hazard: extra care should be taken if carcinogens,
mutagens, or reproductively toxic materials are present, or if for there are substances for
which there is risk of serious or permanent injury at levels only a little way above the OEL.
On the other hand longer intervals between reassessing compliance with the OELs may be
justified if the workplace is under supervision of a professional hygienist, and there are
stable continuous processes with high levels of engineering control and well defined working
processes with high quality control regimes, with change concentrated mainly in well
defined periods such as controlled maintenance.
These uncertainties underline the importance of the use of qualified and experienced occupational
hygienists in making this sort of judgement (see Introduction).
3.9 Use of the results
As discussed in Section 2.5, the law (and good hygiene practice) requires that exposure should be
kept low, not just below the OEL. But if the OEL is not complied with by the tests in sections 3.4 and
3.6, then prompt remedial action is required. If the group compliance test fails, then attention
should be given to the exposure of the whole SEG, perhaps by redesign of work practices or
improvement of engineering control measures. If the individual compliance test fails, then attention
may have to be given to the work practices, equipment, or local control equipment for individual
workers.
In the individual compliance case, the individuals with high individual exposures will need to be
identified. If several samples have already been taken on individuals, then it may be clear by
inspection where the problems lie. If it is not this obvious, then an individual’s results can be
entered into suitable evaluation software (section 2.2) to estimate where his or her 95th percentile
lies in relation to the OEL. Section 3.4 only requires a minimum of 2 and if possible 3 samples per
worker, and if the individual compliance test fails then more sampling will be required to investigate
further individual exposure.
25
The hygienist may also wish to look again at sources of exposure and efficiency of control measures,
using direct-reading instruments for example. However, discussion of control measures is beyond
the scope of this guidance – see the summary in the Introduction to this document.
26
Chapter 4.
Shortcuts and their limitations
4.1 Shortcut 1: Take a few samples from the most exposed worker and use
evaluation software
Advantage
Evaluation software (see section 2.2) can be used to very roughly quantify the exposure in relation to
the OEL from a small number of samples.
Limitation
This depends on identifying the most-exposed workers, and failing to do so means that the approach
gives false confidence. The approach does not give the overall picture that is obtained by calculating
the group and individual compliances. Moreover any conclusions about relation of individual
exposures to the OEL are very uncertain unless many measurements are taken, in which case the
shortcut loses its point.
Outline
It is of course possible simply to take a small number of samples and enter them into software such
as IHSTAT or HYGINIST – see section 2.2. This can be done without going through the process in
chapter 3. Bearing in mind that OELs apply to all workers, the highest-exposed workers in a SEG
should be identified and included, perhaps using a direct-reading instrument to see where the
strongest sources are. Then the software can be used to estimate the distribution of exposures for
each worker who might be at significant risk of exceeding the OEL. But the above limitations make
the results very uncertain.
4.2 Shortcut 2. Taking a few samples and seeing if they are < OEL/3
Advantage
The principle appears in guidance from the British Health and Safety Executive (HSE, 2006). Provided
that a dozen or more samples are taken on the most exposed workers, that the results are
lognormally distributed, and that at least three quarters are below one-third of the OEL, the method
will work.
Limitations
Although this rule was seen as helpful when published, later work shows that it is not a shortcut,
because to give a reasonably reliable result it needs as many samples as the more statistically valid
tests in Chapter 3. As with shortcut 1, it depends on identifying the most-exposed workers, and
failing to do so means that the approach gives false confidence. The approach does not give the
overall picture that is obtained by calculating the group and individual compliances.
27
Outline
From the point of view of dealing with enforcement authorities, this approach has the practical
advantage of being mentioned in the British Health and Safety Executive’s COSHH Essentials
guidance sheet on air sampling, which advises employers, “If the results for a given task are below
one third of the exposure limit, your controls are probably good enough” (HSE, 2006). At first sight
this looks like a useful rule of thumb. It is true that if the exposures are lognormally distributed with
a geometric standard deviation (GSD) of 2.5, then if 75% of exposures are less than one-third of the
OEL only about 3% will be above the OEL. (A GSD of 2.5 is close to the median found by Kromhout et
al. (1993), for SEGs defined by workplace and job title. More precisely-defined SEGs would have
lower GSDs and a smaller percentage above the OEL if this rule were applied.)
The flaw with HSE (2006) is that it gives no guidance on how many samples should be taken, and the
monitoring-averse employer may take as few as possible. Three results of say 0.1, 0.2, and 0.3 give
poor confidence of compliance with an OEL of 1.0. Putting these figures in IHSTAT (see section 2.2)
shows that there is more than a 30% chance that 5% of the distribution lies above the OEL. IHSTAT
can be used to explore the effect of more samples, and by the time a dozen samples have been
obtained with three-quarters below one-third of the OEL, then there is a high degree of confidence
that the OEL is complied with. This assumes that the log-normal assumption is met and that the
most exposed workers have been identified and that it is their exposure that is measured.
But if that many samples are taken, it is no longer a shortcut: the tests in Chapter 3 can be used.
4.3 Shortcut 3. AIHA and Bayes
Advantage
Potentially a powerful approach to exposure surveys, and likely to be a very useful tool in managing
workplaces to comply with OELs.
Limitation
Decisions depend to a certain extent on the hygienist’s professional judgement, which an enforcer
might not accept.
Outline
Hewett et al (2006) and Ramachandran (2008) have described a method of applying Bayesian
statistics to the American Industrial Hygiene Association (AIHA) exposure classification system. It is a
major development in the approach to control in relation to OELs, but as it stands it does not seem
to give us a method of quantifying compliance.
The approach is based on exposure classifications illustrated in the Table.
28
Exposure category
Statistical interpretation
Cat 1
95th percentile < 0.01 x OEL
Cat 2
0.01 x OEL < 95th percentile < 0.1 x OEL
Cat 3
0. 1 x OEL < 95th percentile < 0.5 x OEL
Cat 4
0.5 x OEL < 95th percentile < OEL
Cat 5
95th percentile > OEL
(95th percentile means the upper 95th percentile of the exposure distribution)
The method involves the hygienist using professional judgment and experience to estimate the
fraction of exposures which would be expected to fall in each category (the prior distribution), and
then taking some measurements and putting them in the categories to form a likelihood distribution.
Software is available which combines these using Bayesian methods to form a posterior distribution.
If the professional judgement is good, this method of testing and refinement by measurements
should give a good picture of reality with relatively few measurements. Also, Logan et al (2009) have
shown that the professional judgement can be improved by systematic feedback of results.
Applied as described by Ramachandran (2008), and combined with examination of control practice
as outlined in the Introduction, this may be a powerful method of approaching exposure in the
workplace. Also, if the outcome of this process is, say, < 5% of the posterior distribution in Category
5, then we can have reasonable confidence that the OEL is complied with. The problem for our
purpose is that an enforcer may not regard professional judgement as acceptable evidence, and
without this component the method becomes similar to Shortcut 1 above. However, in a
preliminary review of exposures this could be an efficient method of establishing which SEGs are
likely to have difficulty complying with the OEL.
For those who wish to try it, freeware can be downloaded from the Exposure Assessment Solutions
website http://www.oesh.com . Being freeware, this is not supported and no liability is accepted,
and the user does so at their own risk. This applies also to the following instructions.

Go to http://www.oesh.com and click the software downloads link, and then IH DataAnalyst
Lite. You have to register.

When you have installed and open the programme, a window opens. Click the BDA Initial
Rating tab, check "Custom Professional Judgement Prior", and you can then enter in the
boxes the estimated probabilities of exposures being the above AIHA categories.

Then, when measurements are available, go to the Data tab, enter an OEL, and, in the Conc
column, enter the measured exposures.

Then click the BDA Charts tab. This displays (top) the prior distribution that you estimated,
(middle) the likelihood distribution calculated by the programme from the data you entered,
and (bottom) the Bayesian combination of these as the posterior distribution.
29
Appendix 1. Calculations for the group
and individual compliance tests.
This Appendix gives calculation methods for the group and individual compliance tests, as described
in Section 3.4 to 3.6.
A1.1 SPEED
The Institute of Risk Assessment Sciences at the University of Utrecht and collaborators have
developed a programme called SPEED which does the sort of calculations necessary. This is available
from http://www.iras.uu.nl/iras_speed.php . At the time of writing, the only available version is
based on earlier versions of Microsoft Excel, and does not work with later versions. A new version of
SPEED is being written, which is based on R, and this should make it independent of the version of
Excel or Windows.
When the new version of SPEED becomes available, it is expected to be easier to operate than the
Excel version given below, and being simpler to operate there should be less chance of making a
mistake. However, most hygienists or employers will have Excel, or the OpenOffice equivalent, and
many organisations are reluctant to allow third-party software. An Excel route to the calculation is
therefore given. This will also enable those interested to see how the parameters are derived.
A1.2 Excel method
The example that follows was developed using Microsoft Excel 2007 and Microsoft Windows Vista,
but it runs unchanged on Excel 2010 and Windows 7. It should be easily adaptable to earlier
versions of Excel – see Excel help. It can probably also be readily adapted to the Excel-like
spreadsheet in the Sun Systems free software OpenOffice http://why.openoffice.org/ , although we
have not tested this calculation in OpenOffice. In Excel, the “Analysis Toolpak” must be enabled –
see Excel help on how to do this, and if you search for it, take care with the spelling of Toolpak.
A1.2.1 Entering the values
As an example we have considered a SEG of three workers, who have their personal exposures to
cotton dust measured. The (fictional) results are shown in Fig A1. Two of the workers were
measured four times but Chloe was not working in the SEG on Tuesday and Wednesday, so there are
only two measurements for her. The measurements will only represent the exposure if there is no
systematic variation of exposure with the day of the week, and the measurements must be
representative of the usual exposure if the results are to be valid.
30
If any of the results are below the level of quantification LoQ, see section 3.7.
So the first step is to type in the data on a spreadsheet workbook. Fig A1 shows the example we will
use.
Fig A1 The data – personal exposures to cotton dust for three staff.
The next step is to calculate the natural logarithm of each of these values. As explained in the main
text, the data are assumed to be lognormally distributed, so we have to work with the logged values,
because the analysis works with values that are normally distributed. The process is shown in Fig A2.
We have prepared headings for the table of the log values to the right of the original data, and now
use an Excel maths function, typing =LN(C5) in cell H5. This produces in H5 the natural log of the
value in cell C5.
Throughout this appendix, we will be using natural logarithms, designated LN in Excel, not
logarithms to the base 10. For brevity, we often refer to the logarithm of a value as the logged
value. The number of decimal places displayed in each cell depends on setting under the Home tab,
and in the example cells H5 to J8 are set to display two decimal places, but Excel stores numbers to
many more decimal places and uses them in calculation.2
2
After the Figs in this Appendix were made, it was found that simulated measurements had been entered in
cells D7, D8, and E8 to more decimal places than the two displayed here. This means that if the reader tries to
reproduce this example, some of the calculations will give different numbers in the third or later decimal
places from those in the Figs. This has no effect, but is mentioned in case it causes confusion.
31
Fig A2 Two stages in the calculation of the log-transformed values.
We then click on cell H5, and move the cursor to the bottom right hand corner of this cell, when the
cursor should change to a thin black cross. Hold down the left button of the mouse, and drag the
cross over to the bottom right hand corner of cell J5 (Chloe on Monday) and then down to the
bottom right hand corner of cell J8 (Chloe on Thursday). Fig A2b shows this process half completed.
This should fill cells H5 to J8 with the natural logarithms of the original cotton exposures in cells C5
to E8. It is necessary to delete the error signs in J6 and J7, which appear because the log of zero
cannot be calculated. The completed table is shown in Fig A3.
32
Fig A3 The table of Log values completed
A1.2.2. Group compliance calculation
We can now use these logged values to test group compliance, as explained in Section 3.4 of the
main text. The first step is to calculate the logs of the geometric mean MG and the geometric
standard deviation sG as defined by equations 1 and 2 in section 3.4. In practice we can do this using
two of the functions built in to Excel. In Fig A4 we have started to put log MG in cell H10, by typing in
that cell
=average(
Fig A4 Calculation of log MG
33
which calls up the Excel averaging function, and using the mouse to select the cells H5 to J8, which
contain the values we want to average. If we then hit the return key the average of these logged
values is put into cell H10, as required. We have also typed reminder labels into G10 and G11 for the
functions we are calculating. The log of the geometric mean, which we have just calculated, is equal
to the mean of the logged exposure values. This follows from the definition of the geometric mean.
As shown in Section 3.4 equation 2, log sG is the standard deviation of the logged values, and we put
that in cell H11 by typing
=stdev(
in that cell and again selecting cells H5 to J8 and hitting return. The outcome is shown in Fig A5.
Fig A5 Log MG and log sG calculated
We are now in a position to test group compliance by the procedure in Section 3.4 in the main text.
As in Section 2.1, we will assume for the purposes of illustration that the applicable OEL is 1.7
mg/m3, and we will put this value in cell K10 with a label in J10 to remind us (Fig A6). (1.7 mg/m3 is
an arbitrary choice, and as far as we know this OEL is not use for cotton dust anywhere.) We will
apply equation (3) in Section 3.4 to calculate the parameter U, and we will use the calculation ability
of Excel to put it in cell H12, calling up the values of log MG and log sG from cells H10 and H11, and
the OEL from K10. Fig A6a shows the calculation in progress and Fig A6b shows it complete.
Fig A6b shows that in this example U = 2.80. Referring to Table 1 in Section 3.4, it will be seen that
by the group compliance test the OEL is regarded as complied with if U > 2.005 for 10 exposure
measurements. Clearly there is compliance in this case. Comparing the postulated OEL of 1.7
mg/m3 with the (unlogged) exposure values in Fig A1, this is not surprising. With these exposure
results, the OEL has to fall to 1.1 before U falls below 2.005 and a non-compliance decision is
reached. Again comparing 1.1 with the exposure values in Fig A1, it is not obvious that a statisticallyvalid procedure would give this result.
34
Having reached a compliance decision by the group compliance test, we now have to perform an
analysis of variance to test individual compliance.
.
Fig A6. Calculation of the parameter U
A1.2.3 Analysis of variance (ANOVA)
We are now ready to do the necessary analysis of variance. At the top of the ribbon at the top of the
worksheet, click the Data tab, then in the Analysis group at the right-hand end of the ribbon, click
Data Analysis (in Excel 2002, this is in Tools). (If “Data Analysis” is not visible, it may be because the
Analysis Toolpak is not yet installed – see Excel help.) This produces a window listing various
statistical tests. Fig A7 shows this window. We select ANOVA:Single Factor, and click OK.
35
Fig A7 Selecting the ANOVA function
Selecting the ANOVA function produces the window shown in Fig A8. We click in the Input Range
slot and type in (or select with the mouse) the cell locations of our table of logged values.
Fig A8 Selecting the input data
36
Then we check the button against Output Range, and in the that slot we type the location of the top
left hand of the area where we would like the results to be displayed. In this case, we choose cell
M13 (Fig A9). (Instead of typing, we can click in the Output Range slot, and then click in cell M13.)
Now we are ready to click OK, and the results of the Analysis of Variance are displayed (Fig A10).
Fig A9. Selecting the Output Range – the place where the results will be displayed.
For our purpose we only need some of the results in the analysis of variance (ANOVA) table. (A full
explanation of it can be found in any statistics textbook, for example Wonnacott and Wonnacott,
1990.) We will use them to calculate the within-worker and between-worker variances. For
explanation of the calculations, see Rappaport and Kupper (2008), p 47.
37
Fig A10 The results of the Analysis of Variance. (We have broadened column M so that the titles of
the rows in the ANOVA are completely visible)
A1.2.4 Within-worker variance
The within-worker variance is estimated by the mean square (MS) figure in the “Within Groups” row
of the ANOVA table, ie cell P25 of Fig A10, from which we can see that the variance is 0.257708 in
this case. For convenience we will put this in cell O3. In O3, type
=P25
In N3, type sw2, to remind us that this is the within-worker variance. Fig A11 shows the resulting
display.
38
Fig A11 Displaying the within-worker variance in cell O3
We will later need the within-worker standard deviation, which is the square root of the variance.
We can get Excel to calculate this and to put the answer in cell O4 by typing
=sqrt(O3)
in O4. Fig A12 shows the result, with a label added in N4.
39
Fig A12. Calculation of the within-worker standard deviation.
A1.2.5 Between-worker variance
To calculate the between-worker statistics we first need the between-worker mean square (MSB).
This is already calculated by Excel, and appears in as the Between Groups MS in the ANOVA table.
This is in cell P24 in Fig A11, which in this case shows the figure 0.43988. As in Section 3.4, we
designate the within-worker and between-worker standard deviations as sw and sb respectively; the
corresponding variances are the squares of these. If we had taken the same number of exposure
measurements n0 from each person in the SEG, then MSB would be given by
MSB = sw2 + n0 sb2
(A1)
(Rappaport and Kupper, 2008, Table 5.2.4), and then
sb2 = ( MSB - sw2 ) / n0
(A2)
Our example is rather more complicated, and probably more realistic, because we could not get all
the people we wished to measure present on every shift. In this case, n0 is given by
–
(A3)
where N is the total number of measurements, k the number of people sampled, and ni is the
number of exposure measurements made of the ith person (Rappaport and Kupper, 2008, p 47). The
factor
is the sum of the squares of the number of samples taken for the individual workers.
40
In our example, we have 4 measurements for Joe, 4 for Greg, and 2 for Chloe, so
22.
= 42 + 4 2 +
Fig A13. Calculating the weighted equivalent number of measurements per person, n0
In Fig A13, we have for clarity put into cells Q3 to Q7 the names of variables on the right hand side
of equation A3, and in cells R3 to R7 we have put their values. Then in cell R8 we have calculated the
value of n0 , by typing in the cell the formula which appears in the formula line at the top, which is a
transcription of equation A3, calling up the values in cells R3 to R7.
We can now use equation A2 to calculate the between-person variance sb2, remembering that the
between-worker mean square MSB is in the ANOVA table, and using the value of n0 that we have
just calculated. We will put the between-worker variance sb2 in cell O5, using Excel to do the
calculation, and then put its square root, the between-worker standard deviation, in O6, with the
appropriate labels in N5 and N6 (Figs A14a and A14b)
Because we are only estimating the variances from a limited number of measurements, it sometimes
happens that our estimate of MSB will be less than our estimate of the within-worker variance (MSB
< sw2 ), so that the calculation in Fig A14a results in a negative value for the estimate of the
between-worker variance sb2. What this means is that the true value of the between-worker
variance is probably small; we are only estimating the parameter and our estimate happens to have
come out negative. It is conventional in such a case to set it to zero (Rappaport and Kupper, 2008,
p46).
41
Fig. Calculation of the between-worker variance and standard deviation in cells O5 and O6
A1.2.6 Is the individual compliance test needed in this case?
As explained in section 3.6, individual compliance should be tested if the between-worker variance is
more than 20% of the total variance (sb2 > 0.2 s2), because this indicates that differences in exposure
42
patterns of the individuals in the SEG may be important, so that some individuals in the group may
have exposures exceeding the exposure limit even though the group as a whole is complying.
The total variance is the sum of the between-worker and within worker variances. In Fig A15 this
has been calculated in cell O7. It can be seen that the between-worker variance in cell O5 (0.057
approximately) is less than 20% of the total variance in O7 (0.315), and therefore under our
suggested rule there is no need to proceed to test individual compliance. (Although for clarity we
have calculated the total variance, this was not really necessary. The way we calculated total
variance makes it clear that the test sb2 < 0.2 s2 is equivalent to sb2 < 0.25 sw2 , which can be seen
by comparing cells O5 and O3 in Fig A14b.)
Although in this example we do not need to test individual compliance, we will illustrate the
calculation.
Fig A15. Calculation of total variance
A1.2.7 Testing individual compliance
We will now test individual compliance, by calculating the probability of an individual member of the
SEG having more than 5% of exposures >OEL. We follow the procedure in Hewett (2005), Appendix
A. We need the mean of the distribution of logged values. We previously calculated this as log MG
and put it in cell H10. In doing so, we disregarded the fact that we had more measurements from
Greg and Joe than from Chloe – we effectively assumed that all the workers had the same
distribution, as implicitly assumed in the French procedure we followed (France, 2009). As we are
now considering the possibility that the workers’ exposure distributions may be different, we will
estimate the mean of the whole group as the mean of the individual worker means, which are
displayed in the ANOVA summary in cells P17 to 19 (Fig A14). However, in most cases the difference
between the two ways of estimating the overall mean will be small – about 1.3 % in this example. In
43
Fig A16 we have calculated this new estimate of the mean of the logs in cell O8 and labelled it M in
N8.
Fig A16. Entering the mean of the logged values, M
44
We now calculate a parameter H, in accordance with Section 3.6.
H
=
[ log(OEL) - ( M + 1.645 sw ) ] / sb
(A4)
It will be seen that instead of the overall standard deviation s, we are now using the within- and
between-worker standard deviations which we calculated above. We put this in cell O9, with the
label in N9.
Fig A17. Calculation of parameter H
We use H to estimate the fraction of workers in the SEG having 95th percentiles greater than the OEL,
called here individual exceedance. We do this using the Excel statistical function NORMSDIST. (This
must be typed with care, as there is another Excel function NORMDIST which we do not want.) Fig
45
A18 shows this calculated in cell O10, with a label in M10 as usual. The formula line at the top of Fig
A18 shows what was actually typed in O10.
Fig A18. Calculation of the individual exceedance
It will be seen that the individual exceedance is calculated to be 0.0015, or 0.15%. This means that
that it is estimated that 0.15% of workers in the SEG would be expected to have more than 5% of
their exposures above the OEL. As explained in the main text (Section 3.6) we propose that the
individual compliance test is passed if the individual exceedance is less than 0.2 (ie, that there was a
less than 20% chance of any individual in the group having more than 5% of exposures above the
OEL).
A1.2.8 Discussion of the individual compliance result
We had already concluded (section A1.2.6) that in this example there was little evidence that the
individuals had different exposure patterns, and the individual compliance did not need to be tested,
and the calculation confirms that in this case this test adds nothing to our decision based on the
group compliance test. In the section on group compliance (section A1.2.2), we mentioned that the
exposures would fail that test if the OEL was 1.1 mg/m3 or less. Putting different values for the OEL
in K10, we find that If the OEL is 1.1, the individual exceedance is 12.8%, and if the OEL is 1 mg/m3,
the individual exceedance is 23.0%. This shows that the individual compliance test would fail for
about the same OEL as our group compliance test.
It may seem strange to say that “0.15% of workers in the SEG would be expected to have more than
5% of their exposures above the OEL” when there are only 3 workers in this SEG, but of course we
this is just a more accessible way of making a probability statement. More formally, it means that on
the basis of these results, we estimate that there is only a 0.15% chance of a random worker in the
SEG having more than 5% of exposures greater than the OEL.
46
Once again, we draw attention to the explanation in the Introduction to this guidance that European
law requires effective control, and that compliance with the OEL is not enough.
47
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Amendment history
20 Dec 2011
Preface.
Section 2.2.
Sections 2.5 and 3.6
Amendment of NVvA participants list at the end.
Update of IHSTAT URL
Typing errors
51